Proving countability from surjectivity

let f: S --> T be a surjective function
if S is countable, prove that T is countable

I see that f(S) = T, but and I know that there is a surjection from the natural numbers to S, and an injection from S to N, but I'm not really sure where to head to show that T is countable...Please help

let f: S --> T be a surjective function
if S is countable, prove that T is countable.

Though this answer is a bit late, it may help someone.
This is a well known theorem: is injective if and only if there is a surjection .
Because you are given that is a surjection then by the theorem there is an injection .
Also because S is countable then there in an injection .
Hence is an injection, proving that T is countable.